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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

You were there when I answered John Franklin's question. It was so easy he picked up on it right away. Do you need more than that?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

Ok, I get that one, but look at this problem;

You have ten pigeons and you have to arrange them into three cages so that in every cage the is at least 1 pigeon.You can assume the pigeons to be all the same.the same goes for the cages.In how many ways can you arrange the pigeons into cages under the given conditions?

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi;

There are 36 ways.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

How did you get that?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

You are trying to solve the diophantine equation

a+b+c=10 with 0<a,b,c<11

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

That's pretty much it.But how do you arrive at the answer with GF's?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Now check the coefficient of x^10.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

But what about the condition that there of at least one pigeon on each cage?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi;

Took a while to edit post #82. The polynomial takes that into account automatically.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

So we just take out the 1.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Yes. The 1 represents x^0. There is no 0 choice because there must be at least one pigeon per box.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

Hi bobbym

Then I'm clear on that part.Just have one question.For the x^10 we use asymptotic analysis on the forum right? But, when I do these problems when I'm not allowed to use Wolfram and that stuff, how do I then get the Laurent series?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

You do not need a Laurent series here. There are ways that help you get the coefficients we need. But they are rather limited. There are limits to what can be done by hand.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

And what's that way? And what if I wanted the answer in binomial form?

Btw, do you know what Eurovision is?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi;

The other method would be to use series methods on

it does not look very promising though.

I have not heard of Eurovision.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

Ok, but if I wanted it in the binomial form?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Then you would have to solve the diophantine equation using the formula.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

But is there a way to get it directly out of the GF?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

In this case you could play spot the pattern with the generating function. Other methods do not look promising.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

Ok, then.When can we expect more problems?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

As soon as I get back here.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

Back where?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Back in the forum. I have some work to do.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

So where's the problem?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

**Baffler #2**

**A ship is sailing on a course from the origin. It follows the path y= 3.14 x. It has a speed of 1 / 3 units per second. A submarine is located at (5,0). The sub knows the ship is oblivious to its existence. The sub would like to torpedo the warship. Torpedoes travel at 1 / 2 units per second and travel in straight lines. The sub commander's hobby is mathematics. He fires and sinks the ship! What is the equation of the torpedoes flight?**

**A says) Too easy, here is the answer!**

**B says) I am astounded, you got the right answer!**

**C says) A is my hero.**

**D says) Hip hip hooray!**

**E says) Even a blind squirrel finds an acorn now and then.**

**B says) How true.**

**Find that equation. If A got it then so should you!**

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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